Finite Group Databasebeta

← C5×#13093 #11935813

Subgroups — C5×#13093 #11935813

Order 1280.

752 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#413C211yesmaximal, characteristic, complemented
2C5×#2431C211yesmaximal, characteristic
3C2×C5×#355C212yesmaximal, complemented
4C5×#1785C211yesmaximal, characteristic, complemented
5C5×#1394C212yesmaximal, complemented
6C22×C5×#41C2211yescharacteristic
7C22×C5×M16—21no—
8C2×C5×#127C411yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C2×C5×#121C411yescharacteristic
11C5×#413—24no—
12C2×C5×#101C2212yes—
13C2×C5×#101C2212yes—
14C2×C5×#100—21no—
15C2×C5×#100—21no—
16C5×#407—21no—
17C5×#392—21no—
18C5×#392—21no—
19C5×#391C2211yescharacteristic
20C5×#390C411yescharacteristic
21C5×#386—21no—
22C5×#386—21no—
23C4×C5×C22⋊C4C411yescharacteristic
24C5×#355—24no—
25#13093C511yesmaximal, characteristic, direct product factor, Sylow
26C2×C5×#41—22no—
27C2×C5×#41—22no—
28C2×C5×#41—41no—
29C2×C5×#41—41no—
30C2×C5×#41—42no—
31C22×C5×Q8C2311yescharacteristic
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4C2×C411yescharacteristic
36C22×C5×D4C2×C411yescharacteristic
37C22×C5×D4D411yescharacteristic
38C22×C5×D4D411yescharacteristic
39C23×C4×C5C2×C411yescharacteristic
40C23×C4×C5D411yescharacteristic
41C23×C4×C5D411yescharacteristic
42C2×C5×M16—24no—
43C2×C5×M16—22no—
44C2×C5×M16—22no—
45C2×C5×M16—42no—
46C2×C5×M16—41no—
47C22×C5×C8—41no—
48C5×#127—42no—
49C5×#124—22no—
50C5×#124—22no—
51C5×#121—41no—
52C5×#121—41no—
53C2×C5×C4⋊C4C2×C411yescharacteristic
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C42×C5C2×C411yescharacteristic
61C2×C42×C5C2×C411yescharacteristic
62C5×#101—22no—
63C5×#101—22no—
64C5×#101—22no—
65C5×#101D414yescomplemented
66C5×#100—24no—
67C5×#100—42no—
68C5×C22⋊C8—41no—
69C5×C22⋊C8—41no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C2×#413C2×C511yescharacteristic, complemented
74#2431C2×C511yescharacteristic
75C2×#355C2×C512yescomplemented
76#1785C2×C511yescharacteristic, complemented
77#1394C2×C512yescomplemented
78C24×C5—21no—
79C24×C5C22⋊C411yescharacteristic
80C24×C5C22⋊C411yescharacteristic
81C24×C5C22⋊C411yescharacteristic
82C5×#41—44no—
83C5×#41—44no—
84C5×#41—44no—
85C5×#41—44no—
86C2×C5×Q8—41no—
87C2×C5×Q8—41no—
88C2×C5×Q8C2×D412yes—
89C2×C5×Q8#4112yes—
90C2×C5×D4—22no—
91C2×C5×D4—22no—
92C2×C5×D4—22no—
93C2×C5×D4—22no—
94C2×C5×D4—21no—
95C2×C5×D4—22no—
96C2×C5×D4—21no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—42no—
104C2×C5×D4—42no—
105C2×C5×D4—42no—
106C2×C5×D4—42no—
107C2×C5×D4—42no—
108C2×C5×D4—81no—
109C2×C5×D4—81no—
110C2×C5×D4—81no—
111C2×C5×D4—81no—
112C22×C4×C5—22no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5C22⋊C411yescharacteristic
129C22×C4×C5C22×C411yescharacteristic
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5C2×D411yescharacteristic
132C5×M16—24no—
133C5×M16—44no—
134C5×M16—42no—
135C5×M16—42no—
136C5×M16—42no—
137C2×C5×C8—44no—
138C2×C5×C8—42no—
139C2×C5×C8—42no—
140C5×C4⋊C4—41no—
141C5×C22⋊C4—42no—
142C5×C22⋊C4—41no—
143C5×C22⋊C4—41no—
144C5×C22⋊C4—41no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—41no—
147C5×C22⋊C4—81no—
148C5×C22⋊C4—81no—
149C42×C5—22no—
150C42×C5—41no—
151C22×#41C22×C511yescharacteristic
152C22×M16—21no—
153C2×#127C4×C511yescharacteristic
154C2×#124C22×C511yescharacteristic
155C2×#121C4×C511yescharacteristic
156#413—24no—
157C2×#101C22×C512yes—
158C2×#101C22×C512yes—
159C2×#100—21no—
160C2×#100—21no—
161#407—21no—
162#392—21no—
163#392—21no—
164#391C22×C511yescharacteristic
165#390C4×C511yescharacteristic
166#386—21no—
167#386—21no—
168C4×C22⋊C4C4×C511yescharacteristic
169#355—24no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—21no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—21no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—41no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5—41no—
186C23×C5—41no—
187C23×C5—41no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5#9912yes—
192C23×C5C2×C22⋊C411yescharacteristic
193C5×Q8—42no—
194C5×Q8—42no—
195C5×D4—44no—
196C5×D4—44no—
197C5×D4—42no—
198C5×D4—42no—
199C5×D4—82no—
200C5×D4—84no—
201C5×D4—84no—
202C5×D4—84no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—22no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5#9911yescharacteristic
229C2×C4×C5#9911yescharacteristic
230C2×C4×C5C4×D412yes—
231C2×C4×C5#12011yescharacteristic
232C2×C4×C5#12112yes—
233C2×C4×C5#12311yescharacteristic
234C5×C8—44no—
235C5×C8—82no—
236C2×#41—22no—
237C2×#41—22no—
238C2×#41—41no—
239C2×#41—41no—
240C2×#41—42no—
241C22×Q8C23×C511yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C2×C4×C511yescharacteristic
246C22×D4C2×C4×C511yescharacteristic
247C22×D4C5×D411yescharacteristic
248C22×D4C5×D411yescharacteristic
249C23×C4C2×C4×C511yescharacteristic
250C23×C4C5×D411yescharacteristic
251C23×C4C5×D411yescharacteristic
252C2×M16—24no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16—42no—
256C2×M16—41no—
257C22×C8—41no—
258#127—42no—
259#124—22no—
260#124—22no—
261#121—41no—
262#121—41no—
263C2×C4⋊C4C2×C4×C511yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42C2×C4×C511yescharacteristic
271C2×C42C2×C4×C511yescharacteristic
272#101—22no—
273#101—22no—
274#101—22no—
275#101C5×D414yescomplemented
276#100—24no—
277#100—42no—
278C22⋊C8—41no—
279C22⋊C8—41no—
280#95—21no—
281#95—21no—
282#95—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—22no—
286C22×C5—42no—
287C22×C5—42no—
288C22×C5—41no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—41no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5—81no—
297C22×C5—81no—
298C22×C5—81no—
299C22×C5—81no—
300C22×C5—81no—
301C22×C5—81no—
302C22×C5—81no—
303C22×C5—81no—
304C22×C5—81no—
305C22×C5—81no—
306C22×C5—81no—
307C22×C5#38611yescharacteristic
308C22×C5C2×#9911yescharacteristic
309C22×C5C2×#9911yescharacteristic
310C4×C5—21no—
311C4×C5—22no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—22no—
316C4×C5—42no—
317C4×C5—81no—
318C4×C5—81no—
319C24—21no—
320C24C5×C22⋊C411yescharacteristic
321C24C5×C22⋊C411yescharacteristic
322C24C5×C22⋊C411yescharacteristic
323#41—44no—
324#41—44no—
325#41—44no—
326#41—44no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8C2×C5×D412yes—
330C2×Q8C5×#4112yes—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4—81no—
350C2×D4—81no—
351C2×D4—81no—
352C2×D4—81no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4C5×C22⋊C411yescharacteristic
370C22×C4C22×C4×C511yescharacteristic
371C22×C4C2×C5×D411yescharacteristic
372C22×C4C2×C5×D411yescharacteristic
373M16—24no—
374M16—44no—
375M16—42no—
376M16—42no—
377M16—42no—
378C2×C8—44no—
379C2×C8—42no—
380C2×C8—42no—
381C4⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—41no—
384C22⋊C4—42no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—81no—
389C22⋊C4—81no—
390C42—22no—
391C42—41no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—42no—
395C2×C5—81no—
396C2×C5—81no—
397C2×C5—161no—
398C2×C5#189811yescharacteristic
399C2×C5#213211yescharacteristic
400C2×C5#213411yescharacteristic
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23C5×#9912yes—
423C23C2×C5×C22⋊C411yescharacteristic
424Q8—42no—
425Q8—42no—
426D4—44no—
427D4—44no—
428D4—42no—
429D4—42no—
430D4—82no—
431D4—84no—
432D4—84no—
433D4—84no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4C5×#9911yescharacteristic
460C2×C4C5×#9911yescharacteristic
461C2×C4C4×C5×D412yes—
462C2×C4C5×#12011yescharacteristic
463C2×C4C5×#12112yes—
464C2×C4C5×#12311yescharacteristic
465C8—44no—
466C8—82no—
467C5#1309311yescharacteristic, direct product factor, Sylow
468C22—21no—
469C22—21no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22C5×#38611yescharacteristic
493C22C2×C5×#9911yescharacteristic
494C22C2×C5×#9911yescharacteristic
495C4—21no—
496C4—22no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—42no—
502C4—81no—
503C4—81no—
504C2—21no—
505C2—21no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—161no—
510C2C5×#189811yescharacteristic
511C2C5×#213211yescharacteristic
512C2C5×#213411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC5×#2431C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×#413C2semidirect
3. C2×C5×#355C2semidirect
4. C5×#1785C2semidirect
5. C5×#1394C2semidirect
25. #13093C5direct (N × H)
65. C5×#101D4semidirect
73. C2×#413C2×C5semidirect
75. C2×#355C2×C5semidirect
76. #1785C2×C5semidirect
77. #1394C2×C5semidirect
275. #101C5×D4semidirect
467. C5#13093direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×#4132
C5×#24312
C2×C5×#3552
C5×#17852
C5×#13942
#130935